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This paper investigates the concept of harmonic functions of bounded meanoscillation, starting from John-Nirenberg's pioneering studies, under a renewedformalism, suitable for bringing out some fundamental properties inherent init. In more detail: after a quick introduction, the second Section presents themain theorem, plus complete proof, relating to this function; in the thirdSection there is a suggestion on the exponential integrability (theorem andsketch of proof), while the fourth Section deals with the duality of HardySpace $H^1$ and bounded mean oscillation, with some ideas for a demonstration.The writing closes with a graphic appendix.

Bounded Mean Oscillation: an $\mathbb{R}$-Function with Multi-$\mathbb{K}_6$ Cubes. Dual of the Hardy Space $H^1$ and Banach Extent